### Dirichlet to Neumann Maps for Infinite Metric Graphs

Carlson, R *(Colorado)*

Thursday 29 July 2010, 14:45-15.30

Seminar Room 1, Newton Institute

#### Abstract

Motivated by problems of modeling the human circulatory system, boundary value problems for differential operators -D2 + q are considered on the metric completions of infinite graphs with finite volume, finite diameter, or other smallness conditions. For a large family of graphs, the existence of an ample family of simple test functions permits a generalized definition of the Dirichlet to Neumann map taking boundary functions to their normal derivatives. Properties of this map, problems exhibiting more regular derivatives, and approximation by finite subgraphs will be discussed.

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